Plant Factor, load Factor, load Curve and Reliability Indices

Plant factor

The plant factor, also known as the net capacity factor, of a plant, is defined as the ratio of its actual energy output to its potential output if it is operated continuously at its rated capacity over a period of time.In simple words, it is the ratio of the average demand on the power plant to the maximum installed capacity of the plant.

It is given as,

Plant factor (PF) = Average power demand/Installed capacity of the plant

Multiplying the numerator and denominator by some period of time, we get the relationship in terms of energy as in the original definition as,

PF = Energy generated/Energy available

Numerical example:

The following data of a power plant is given:

Installed capacity of the plant (Preinstalled) = 50 MW

Power demand at the plant (P consumed) = 20 MW

Time of energy consumption (T consumed) = 18 hours

Find the plant factor of the plant.

Solution:

The operation is studied for a period of 24 hours. Therefore in a period of 24 hours,

Energy generated = (P_consumed × T_consumed ) = 20 × 18 = 360 MWh

Energy available = ( P_installed × 24) = 50 × 24 = 1200 MWh

Then Plant factor is obtained as,

PF = Energy generated/Energy available

= 360/1200

= 0.3

Load factor

Load factor is defined as the ratio of average load to the peak load. It can also be expressed as the ratio of a number of units supplied during a certain period of the maximum energy demand during that period. Load factor refers to the energy load on a system as compared to its peak load for a given period of time and is most typically calculated on a monthly or annual basis.

Load factor is given as,

Load factor (LF) = Average load/Peak load

= No. of energy units supplied during a particular period/Maximum power demand during that period × Period

Loss factor

It is defined as a factor which when multiplied with energy loss at peak time and the number of loads periods gives the overall average energy loss. It is expressed as the ratio of average power loss to the peak power loss or power loss at peak load. If the load to a power plant is constant, throughout the day, the loss factor of the plant is 1. But in practice, the load to a plant varies throughout the day which is given by a load curve.

An approximate value of loss factor can be found by the following equation:

Loss factor = (0.3 × Load factor) + (0.7) × (Load factor)²

Load curve

A load curve, also known as load profile, is a chart illustrating the variation of electrical load over a period of time. Generating companies or electrical utilities use this chart to study the pattern of load variation and to obtain information regarding the amount of power to be generated at a specific time.

An example of a load curve is given in the figure below.

Numerical example:

The load curve of a power plant for a day is shown in the figure below. Calculate the plant factor, load factor, loss factor, and energy loss in a day if the installed capacity of the plant is 150 MW and energy loss at peak load is 10 MW.

Solution:

According to the load curve,

Total units supplied in a day = (50 × 8) + (80 × 4) + (130 × 5) + (60 × 7) = 1790 units

Therefore, average load = 1790/24 = 74.58 MW

Plant factor = Average load/Installed capacity = 74.58/150 = 0.49

Load factor = Average load/Peak load = 74.58/130 = 0.5736

Loss factor = (0.3 × Load factor) + (0.7) × (Load factor)² = (0.3 × 0.5736) + (0.7) × (0.5736)² = 0.4023

Actual power loss = Power loss at peak load × Loss factor = 10 × 0.4023 = 4.023

Thus, energy loss in a day (24 Hours) = 24 × 4.023 = 96.552 KWh

Reliability indices

Reliability indices are the parameters or numerical values which are used to determine and describe the performance and reliability of an electric power system. Reliability of a transmission and distribution system refers to the ability of the system to perform its normal functions in both normal and abnormal situations. These indices help us to determine how different components of an interconnected system affect the transmission and distribution of electric power in the whole system. The different reliability indices

SAIDI (System Average Interruption Duration Index)

SAIDI is used by the electric utilities to determine the average cut off or interruption of electric power per customer served. It is obtained as:

SAIDI = (∑ (Duration of trip × No. of consumers affected))/Total consumers

SAIFI (System Average Interruption Frequency Index)

SAIFI is used by the electric utilities to determine the average number of power outages per customer. It is obtained as:

SAIFI = (∑ (No. of trip × No. of consumers affected))/Total consumers

CAIDI (Customer Average Interruption Duration Index)

CAIDI is the ratio of SAIDI to SAIFI and is used by the electric utilities to determine the average power interruption duration that customer experiences. It can also be referred to as average restoration time. It is measured in units of time usually over a course of one year. It is obtained as:

CAIDI = SAIDI/SAIFI

ASAI (Average System Availability Index)

It is used by the electric utilities to determine the average availability of electric power in the system. It is also measured for a course of one year and is obtained as:

ASAI = (8760 × Total consumers - ∑ (Duration of trip × No. of consumers affected))/(Total consumers × 8760)

Example: If the ASAI of a system is 0.9563, it shall be known that electric energy is available in the system 95.63% of the time.

Numerical example:

Calculate all the reliability indices of the distribution system as shown in the diagram below. The number of tripping and trip duration are given for a period of one year. (Asked in 2070 Chaitra)

Solution:

According to the question,

Total number of consumers = Total number of consumers for CB M (N) = 6000

Total number of consumers for CB 1 (N_CB1) = 2000

Total number of consumers for CB 2 (N_CB2) = 2500

Total number of consumers for CB 3 (N_CB3) = 1500

Total number of trips for CB M (T_CBM) = 0

Total number of trips for CB 1 (T_CB1) = 100

Total number of trips for CB 2 (T_CB2) = 75

Total number of trips for CB 3 (T_CB3) = 50

Total trip duration for CB M (D_CBM) = 0

Total trip duration for CB 1 (D_CB1) = 150

Total trip duration for CB 2 (D_CB2) = 280

Total trip duration for CB 3 (D_CB3) = 140

We have,

SAIFI = (∑ (No. of trip × No. of consumers affected))/Total consumers

= (T_CBM × N + T_CB1× N_CB1 + T_CB2× N_CB2 + T_CB3× N_CB3)/N

= (0 × 6000 + 100 × 2000 + 75 × 2500 + 50 × 1500)/6000 = 77.083 trips per customer

SAIDI = (∑ (Duration of trip × No. of consumers affected))/Total consumers

= (D_CBM × N + D_CB1× N_CB1 + D_CB2× N_CB2 + D_CB3× N_CB3)/N

= (0 × 6000 + 150 × 2000 + 280 × 2500 + 140 × 1500)/6000 = 201.67 hours per customer

CAIDI = SAIDI/SAIFI = 201.67/77.083 = 2.616 hours per trip

ASAI = (8760 × Total consumers - ∑ (Duration of trip × No. of consumers affected))/(Total consumers × 8760)

= (8760 × 6000 - 1210000)/52560000 = 0.9769 = 97.69%

References

1. Wikipedia. (2016). Retrieved from https://www.wikipedia.org/

Information from the handouts provided by my lecturer Mr. Gopal Joshi Subedi has also been used. The numerical problem of reliability indices has been asked in the regular exam of 2070.

The image of the sample load curve was taken from the research article "Journal of Energy in Southern Africa" by Bernard Tembo and Bruno Merven http://www.scielo.org.za/